Multiple-Point Statistics (MPS) simulation is a facies modeling approach that allows simulation of complex geological patterns, such as sinuous channels, that cannot be modeled using conventional geostatistical variogram-based techniques. MPS simulation consists of first extracting patterns from a training image describing the type of facies heterogeneity expected in the reservoir under study, and then reproducing similar patterns conditionally to well and seismic data in the simulation grid.
SNESIM (Single Normal Equation Simulation) is an MPS simulation program that is well known to those skilled in the art of reservoir modeling. Conventional SNESIM is described in Strebelle, S., 2000, Sequential Simulation of Complex Geological Structures Using Multiple-Point Statistics, doctoral thesis, Stanford University, and Strebelle S., 2002, Conditional Simulation of Complex Geological Structures Using Multiple-Point Statistics: Mathematical Geology, V. 34, No. 1. SNESIM is a direct pixel-based sequential algorithm whereby the unsampled nodes of the stratigraphic grid discretizing the reservoir volume of interest are visited a single time along a random path. At each node, the SNESIM simulation program draws a facies value from the local conditional distribution inferred by looking in the training image for patterns matching the conditioning data located in the neighborhood of the node to be simulated. MPS facies models, just like any type of facies models, are then populated with reservoir properties, typically, porosity, permeability, and water saturation, using variogram-based techniques.
Sequential Gaussian Simulation (SGS) is a variogram-based technique traditionally used to simulate reservoir properties. SGSIM, which is described in Deutsch C., and Journel, A. (1998) GSLIB: Geostatistical Software Library and User's Guide, second edition, Oxford University Press, is a SGS simulation program that is well known to those skilled in the art of reservoir modeling. SGS, however, as any type of variogram-based technique, does not allow reproducing reservoir property trends, in particular intra-facies geobody trends. Intra-facies geobody petrophysical trends, such as decreasing porosity and permeability from channel axis to channel margins in channelized reservoirs, are commonly observed, and they may have a significant impact on reservoir flow behavior.
This problem, although commonly recognized by reservoir modelers, remains unsolved. In view of the foregoing, a need exists for a method for simulating reservoir property trends, including petrophysical trends within facies geobodies, that addresses the above-identified short comings.